Magnetic resonance imaging (MRI) is a medical imaging technique based on the phenomenon of nuclear magnetic resonance (NMR). In contrast with medical imaging techniques using x-rays, MRI is capable of producing high resolution images for a variety of applications and anatomies without using ionizing radiation. Typically, a MRI scan is initiated by generating a strong magnetic field which aligns the magnetic moments of protons (i.e., the nuclei of hydrogen atoms) in the volume of interest being scanned. A radiofrequency (RF) pulse is then transmitted into the volume of interest. If the frequency of the RF pulse matches the Larmor frequency of protons in the volume, the pulse may induce a spin-flip transition of the protons from an aligned state to a higher-energy anti-aligned state. When the protons relax after the pulse, they will then emit RF signals at the Larmor frequency which can be detected with receiver coils. The intensity of the detected signal is representative of the concentration of protons in the volume.
The Larmor frequency of a proton is proportional to the strength of the magnetic field. Consequently, if the applied magnetic field is generated with a known spatial gradient, then the Larmor frequency of protons will also have a known spatial localization. Because the frequencies of the detected RF signals from the relaxing protons are known (i.e., the signal data is measured in the frequency domain, or k-space), and because these frequencies are correlated with spatial locations through the known magnetic gradient field, the signal can be transformed from the frequency domain to the spatial domain to produce an image. Because the gradient field provides the correlation between the frequency domain and image domain, it is sometimes called an encoding field.
Conventionally, several orthogonal linear gradients are used in MRI, and several repetition times (TRs) are needed to gather sufficient information to reconstruct an image of the volume. Thus, conventional MRI requires relatively long scan times. Consequently, researchers have developed various techniques in attempt to reduce scan times. For example, one recent advance in MRI, known as parallel imaging, involves acquiring signals simultaneously with multiple receive coils. The acquired data can be under-sampled and the resulting aliasing can be unwrapped using receiver coil sensitivity information to produce full images.
Generally, parallel imaging methods combine spatially-weighted data from multiple simultaneous measurements in order to reduce scan time. Most parallel imaging approaches collect a reduced data set for later interpolation for a Fourier or algebraic reconstruction. By relying on the Fourier reconstruction approach, conventional approaches use orthogonal gradients that complement each other. These gradients, however, can be inefficient with regards to information gathered from the coil sensitivities, resulting in longer scan times and/or reduced image resolution.
For an N×N image, a classic fully-sampled linear gradient data collection scheme requires N repetitions of the basic procedure to generate N lines of k-space. During each repetition time, linear magnetic gradients create plane-wave oscillations in the phase across the image. As the phase variation replicates the kernel of the Fourier transform, the k-space data set is reconstructed via the fast Fourier transform (FFT). When k-space lines are undersampled, aliasing occurs as image fold over.
Conventionally, parallel reconstruction operates on an undersampled frequency domain data set, and data sets from separate coils are either combined in the k-space domain, in the image domain, or a hybrid space. GRAPPA, SENSE, and SMASH exemplify three known approaches within a Fourier acquisition scheme using linear magnetic gradients for signal encoding. SMASH uses linear combinations of coil sensitivity profiles as a free parameter to shift existing k-space lines to fit omitted data. In order to shift k-space lines, linear combinations of coil profiles must approximate spatially oscillating functions. In practice, coil sensitivity profiles are slowly varying and spatially distinct. The limited flexibility in changing coil profiles makes implementation on an anatomy-constrained geometry difficult.
In another approach to reducing scan time, some research has aimed to modify receive coils, allowing for less data collection and better unwrapping of the aliasing artifacts. This research has focused on increasing the number of receive coils to localize the sensitivity, only to face issues of ballooning cost and diminishing returns. Recent hardware advances used up to 96 receive coil elements. Hardware costs increase dramatically with the number of coils since each coil must use a separate receiver, cabling, pre-amplifier, and so on. The difficulty of constructing large coil arrays is nontrivial as elements must be de-coupled. Nearest neighbor approaches through overlapping coils and pre-amplifier decoupling partially addresses inductive coupling of numerous further elements. Increasing coil number reduces the g-factor, a pixel by pixel measure of noise amplification, but drives the cost much higher. Moving to higher fields and including spatially selective parallel transmission pulses show promise, but fundamentally does not address the underlying encoding problem.
Improvements have been made in SENSE and GRAPPA reconstructions to preserve reconstruction quality, but these penalize acceleration in image acquisition. There has been a trend towards auto-calibration, which has been adopted by SENSE/SMASH as generalized SENSE/SMASH (GSENSE/GSMASH). Another generalization is the expansion of data sampling trajectories to radial and spiral k-space trajectories. For example in radial k-space sampling, an auto-calibration scan (ACS) is collected near the center of k-space during each readout. Using auto-calibration improves image quality at the expense of imaging time by requiring more data collected, or introduces bias by emphasizing low spatial frequency components of the image.
Though sharing a frequency and phase acquisition scheme with Cartesian data, PatLoc (parallel imaging technique with local gradients) performs orthogonal gradients imaging with nonlinear gradients. Non-bijective curvilinear gradients enable faster gradient switching through dB/dt reduction. PatLoc reconstruction relies on the local orthogonality in the magnetic fields to apply a volumetric correction term to the integrand of the signal integral. With the volumetric correction, the image is reconstructed using a fast Fourier transform (FFT). Limiting gradients to a pair-wise orthogonal multi-polar gradient set causes position dependent resolution, with a noticeable absence of signal localization in the center of the image. To date, higher-order gradient encoding has only been performed using custom-built gradient coils.